Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past yearsfor fighting vector-borne diseases such as dengue, chikungunya and zika.Several strains of this bacterium cause cytoplasmic incompatibility (CI) and can also affect their host's fecundity or lifespan, while highly reducing vector competence for the main arboviruses.

We consider and answer the following questions: 1) what should be the initial condition (i.e. size of the initial mosquito population) to have invasion with one mosquito release source? We note that it is hard to have an invasion in such case. 2) How many release points does one need to have sufficiently high probability of invasion? 3) What happens if one accounts for uncertainty in the release protocol (e.g. unequal spacing among release points)?

We build a framework based on existing reaction-diffusion models for the uncertainty quantification in this context,obtain both theoretical and numerical lower bounds for the probability of release successand give new quantitative results on the one dimensional case.

Figure 2.
Time dynamics with three different initial releases belonging to the set $RP_{50}^2(N)$ of (10), with $N/(N+N_0) = 0.75$. Integration is performed on the domain $[-L, L]$ with $L = 50 \textrm{km}$. The release box is plotted in dashed red on the first picture of each configuration. Left: Release box $[-2 L/3, 2 L/3]^2$. Center: Release box $[-L/2, L/2]^2$. Right: Release box $[-L/12.5, L/12.5]^2$. From top to bottom: increasing time $t \in \{0, 1, 25, 50, 75\}$, in days. The color indicates the value of $p$ (with the scale on the right).

Figure 3.
Comparison of minimal invasion radii $R_{\alpha}$ (obtained by energy) in dashed line and $L_{\alpha}$ (obtained by critical bubbles)
in solid line, varying with the maximal infection frequency level $\alpha$. The scale is such that $\sigma=1$.